A Train of Length L is Traveling at a Constant Velocity and Passes a Pole GMAT Problem Solving

Question: A train of length L is traveling at a constant velocity and passes a pole in t seconds. If the same train travelling at the same velocity passes a platform in 3t seconds then what is the length of the platform:

A) 0.5 L
B) L
C) 1.5 L
D) 2 L
E) 3 L

Correct Answer: D

Solution and Explanation:
Approach Solution 1:
Length of train= Distance= L
Time to cross the pole= time= t
So speed= L/t

New time= 3t. So distance travelled= 3t*L/t= 3L

The distance is equal to train length L+ platform length= 3L
So the platform is 2L.

Approach Solution 2:
We can let p = the length of the platform in metres and r= the rate the train is travelling.

When the train crosses a platform in 3t seconds, it means it takes 3t seconds for the nose of the train to enter one end of the platform and the tail of the train to exit the other end of the platform. Thus, in 3t seconds, not only does the train travel the entire length of the platform but also it travels its body length L. Thus, we have (using time x rate = distance formula):

3t * r = p + L

It is given that the train crosses a pole (notice that the pole has a negligible width) in t seconds. So when the train crosses the pole, it only travels its body length in t seconds. Thus we have:

t * r = L

Subtracting these two equations, we have:

2tr = p

Since L = tr, and p = 2tr, then p = 2L.

Approach Solution 3:

Train passes a pole in T seconds.

In order to pass the pole, the train needs to put its entire length of L from the head of the train to the back of the train in front of the pole. This distance covered will = length of train = L

Speed of Train = (L metres) / (T seconds)

In order to pass the platform, once the head of train reaches the beginning of the platform, the train will need to cover:

distance of the platform (let it be X)
+
put its entire distance in front of the platform (another distance = Length of Train = L)

To pass the platform, the train will therefore need to cover a distance = L + X
where X = length of platform.
The time taken to do this is = 3T seconds

Speed * Time = Distance of Train and Platform

(L/T) * (3T) = L + X
3L = L + X
X = 2L = length of platform

“A train of length L is travelling at a constant velocity and passes a”- is a topic of the GMAT Quantitative reasoning section of GMAT.To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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